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C2×C5×(C13⋊C3)⋊D7 #19129794

order5460
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×(C13⋊C3)⋊D7
unambiguous semidirect product(C2×C13⋊C3)⋊(C5×D7)

Splittings

Fitting, socleC2×C5×C7×C13 ⋊ C2×C3
derived, HallC7×C13 ⋊ C22×C3×C5
HallC2×C5×D91 ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C22
HallC5×C7×C13 ⋊ C22×C3
HallC2×D91 ⋊ C3×C5
HallC7×C13⋊C3 ⋊ C22×C5
HallC5×C13⋊C3 ⋊ C2×D7
HallC5×C13 ⋊ C2×C3×D7
HallC13⋊C3 ⋊ C2×C5×D7
HallC5×C7 ⋊ C2×D13⋊C3
SylowC13 ⋊ C2×C3×C5×D7
SylowC7 ⋊ C2×C5×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5(C13⋊C3)⋊D7
commutator, hypocenterC7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

290 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×ΓL(1,𝔽8)⋊(D13⋊C3), C5×D3×(C13⋊C3)⋊D7, C2×C3×C5×(C13⋊C3)⋊D7, …
maximal normal subgroup ofC2×C5×ΓL(1,𝔽8)⋊(D13⋊C3), C2×C3×C5×(C13⋊C3)⋊D7, C2×C25×(C13⋊C3)⋊D7, …
maximal quotient ofC2×C5×(C13⋊C9)⋊D7, C5×D3×(C13⋊C3)⋊D7, C2×C3×C5×(C13⋊C3)⋊D7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 136);